Question: Luis is 2 times as old as Daniel. 35 years ago, Luis was 7 times as old as Daniel. How old is Daniel now?
Explanation: We can use the given information to write down two equations that describe the ages of Luis and Daniel. Let Luis's current age be $l$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $l = 2d$ 35 years ago, Luis was $l - 35$ years old, and Daniel was $d - 35$ years old. The information in the second sentence can be expressed in the following equation: $l - 35 = 7(d - 35)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to use our first equation for $l$ and substitute it into our second equation. Our first equation is: $l = 2d$ . Substituting this into our second equation, we get: $2d$ $-$ $35 = 7(d - 35)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $2 d - 35 = 7 d - 245$ Solving for $d$ , we get: $5 d = 210.$ $d = 42$.